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Course Code: 
MATH 343
Semester: 
Spring
Course Type: 
Core
P: 
3
Lab: 
0
Laboratuvar Saati: 
0
Credits: 
3
ECTS: 
6
Course Language: 
English
Course Objectives: 
To give the students the formation of Partial Differential Equations, classifications and their solutions at the beginning level.
Course Content: 

First order equations; linear, quasilinear and nonlinear equations. Classification of second order linear partial differential equations, canonical forms, Cauchy problem. The Cauchy problem for the wave equation. Dirichlet and Neumann problems for the Laplace equation, maximum principle. Heat equation on the strip.

Course Methodology: 
1: Lecture, 2: Problem Solving
Course Evaluation Methods: 
A: Written examination, B: Homework

Vertical Tabs

Course Learning Outcomes

Learning Outcomes

TeachingMethods

Assessment Methods

1) Understands the derivation of PDE and modelling

1, 2

A, B

2) Knows the nonlinear equations, their properties and the solution techniques

1, 2

A, B

3) Has a general information on higher order equations and on Cauchy problem

1, 2

A, B

4) Knows the properties of wave equation and the solution techniques of initial value problems

1, 2

A, B

5) Knows the properties of Laplace equation and the solution techniques of boundary value problems

1, 2

A, B

6) Knows the properties of heat equation and the solution techniques of initial value problems

1, 2

A, B

Course Flow

Week

Topics

Study Materials

1

Introduction, First-order DE,

Relevant topics in the text book

2

Introduction, First-order DE,

Relevant topics in the text book

3

First-order nonlinear DE, Compatible systems Charpit’s method

Relevant topics in the text book

4

First-order nonlinear DE, Compatible systems Charpit’s method

Relevant topics in the text book

5

Linear second-order equations; constant  coefficient and factorable operators, particular solutions.                                                                       

Relevant topics in the text book

6

Linear second-order equations; constant  coefficient and factorable operators, particular solutions.                                                                       

Relevant topics in the text book

7

Normal forms; hyperbolic, parabolic, elliptic cases; Cauchy problem.

Relevant topics in the text book

8

Normal forms; hyperbolic, parabolic, elliptic cases; Cauchy problem.

Relevant topics in the text book

9

Elliptic equations

Relevant topics in the text book

10

Elliptic equations

Relevant topics in the text book

11

Hyperbolic equations

Relevant topics in the text book

12

Hyperbolic equations

Relevant topics in the text book

13

Parabolic equations

Relevant topics in the text book

14

Parabolic equations

Relevant topics in the text book

Recommended Sources

Textbook

1. An introduction to PDE and BVP, by Rene Dennemeyer, McGraw Hill.

2.  Elements of PDE, by Ian Sneddon,  McGraw Hill.

Additional Resources

 

Material Sharing

Documents

 

Assignments

 

Exams

 

Assessment

IN-TERM STUDIES

NUMBER

PERCENTAGE

Mid-terms

2

100

Quizzes

0

0

Assignments

3

0

Total

 

100

CONTRIBUTION OF FINAL EXAMINATION TO OVERALL GRADE

 

40

CONTRIBUTION OF IN-TERM STUDIES TO OVERALL GRADE

 

60

Total

 

100

 

COURSE CATEGORY

Expertise/Field Courses

Course’s Contribution to Program

No

Program Learning Outcomes

Contribution

1

2

3

4

5

1

The ability to make computation on the basic topics of mathematics such as limit, derivative, integral, logic, linear algebra and discrete mathematics which provide a basis for the fundamenral research fields in mathematics (i.e., analysis, algebra, differential equations and geometry)

x

 

 

 

 

2

Acquiring fundamental knowledge on fundamental research fields in mathematics

 

 

 

 

x

3

Ability form and interpret the relations between research topics in mathematics

 

 

 

x

 

4

Ability to define, formulate and solve mathematical problems

 

 

 

x

 

5

Consciousness of professional ethics and responsibilty

 

 

 

x

 

6

Ability to communicate actively

x

 

 

 

 

7

Ability of self-development in fields of interest

 

 

 

x

 

8

Ability to learn, choose and use necessary information technologies

x

 

 

 

 

9

Lifelong education

 

 

x

 

 

ECTS

Activities

Quantity

Duration
(Hour)

Total
Workload
(Hour)

Course Duration (14x Total course hours)

14

3

42

Hours for off-the-classroom study (Pre-study, practice)

14

6

84

Mid-terms (Including self study)

2

8

16

Quizzes

 

0

00

Assignments

3

1

3

Final examination (Including self study)

1

15

15

Total Work Load

 

 

160

Total Work Load / 25 (h)

 

 

6.4

ECTS Credit of the Course

 

 

6